Are services seperated between parallel pipeline runs?

I have a perfect running pipeline (a runner in another docker server) with some unit test building upon several services, including some mongo db. As the pipeline gets triggered for each git push, it might happen that I push again the next change before the previous pipeline has finished.
In some occasions I then get errors from the DB service about key collisions etc.

I fear that the service running per pipeline gets reused from the second pipeline, including the temporary test data.

Is that behavior wanted/planned and how to circumvent it? Did anyone name the services dynamically in the pipeline like the running ID as appending part or so?